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<div class="title">ukf_math.h</div>  </div>
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<a href="ukf__math_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* ukf_math.h</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> * Copyright (C) 2011-2014 Jeremy Fix</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> * This program is free software; you can redistribute it and/or modify</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> * it under the terms of the GNU General Public License as published by</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> * the Free Software Foundation; either version 3 of the License, or (at</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> * your option) any later version.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> * This program is distributed in the hope that it will be useful, but</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> * WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> * General Public License for more details.</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> * You should have received a copy of the GNU General Public License</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment"> * along with this program; if not, write to the Free Software</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"> * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#ifndef UKF_MATH_H</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define UKF_MATH_H</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#include &lt;gsl/gsl_vector.h&gt;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#include &lt;gsl/gsl_matrix.h&gt;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">namespace </span>ukf</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;{</div>
<div class="line"><a name="l00032"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html">   32</a></span>&#160;    <span class="keyword">namespace </span>math</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    {</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;</div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#acaa2c088a31957c32107da9c838c77bb">   35</a></span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespaceukf_1_1math.html#acaa2c088a31957c32107da9c838c77bb">min</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b)</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        {</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            <span class="keywordflow">return</span> a &lt; b ? a : b;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        }</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#af4ef51ae6ef8c8d19eba957802834d4d">   40</a></span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespaceukf_1_1math.html#af4ef51ae6ef8c8d19eba957802834d4d">max</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b)</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        {</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;            <span class="keywordflow">return</span> a &lt; b ? b : a;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        }</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#a8123c498310baa12b0985a3bd271c06c">   45</a></span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="namespaceukf_1_1math.html#a8123c498310baa12b0985a3bd271c06c">signof</a>(<span class="keywordtype">double</span> x)</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;        {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            <span class="keywordflow">return</span> x &lt;= 0.0 ? -1.0 : 1.0;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        }</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#a341c355f5fddc026efa8589de2f59a50">   50</a></span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceukf_1_1math.html#a341c355f5fddc026efa8589de2f59a50">cmp_equal</a>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y)</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        {</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            <span class="keywordflow">return</span> fabs(x - y) &lt;= 1e-10;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        }</div>
<div class="line"><a name="l00054"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#a1a77efe08924024899592af61ec193da">   54</a></span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceukf_1_1math.html#a1a77efe08924024899592af61ec193da">cmp_diff</a>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y)</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        {</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;            <span class="keywordflow">return</span> fabs(x - y) &gt;= 1e-10;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        }</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;</div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="namespaceukf_1_1math.html#ac921eed0b4618cb2e860cf712c676675">   64</a></span>&#160;        <span class="keywordtype">void</span> <a class="code" href="namespaceukf_1_1math.html#ac921eed0b4618cb2e860cf712c676675">choleskyUpdate</a>(gsl_matrix * sigmaTheta, <span class="keywordtype">double</span> alpha, gsl_vector *x) {</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            <span class="comment">/*</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">                This function performs a cholesky update of the</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">                cholesky factorization sigmaTheta, that is it replaces</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">                the Cholesky factorization sigmaTheta by the cholesky factorization of</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">                            sigmaTheta*sigmaTheta^T + alpha * x * x^T</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">                The algorithm is an adaptation of a LU factorization rank one update.</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">                Reference is :</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">                Peter Strange, Andreas Griewank and Matthias Bollhöfer.</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment">                On the Efficient Update of Rectangular LU Factorizations subject to Low Rank Modifications.</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">                Electronic Transactions on Numerical Analysis, 26:161-177, 2007.</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">                alg. is given in left part of fig.2.1.</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment">                Perhaps a more efficient algorithm exists, however it should do the work for now. And the code is probably not optimal...</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">            */</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;            <span class="keywordflow">if</span> (sigmaTheta-&gt;size1 != sigmaTheta-&gt;size2)</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                std::cout&lt;&lt;<span class="stringliteral">&quot;ERROR ukf::math::choleskyUpdate Cannot use CholeskyUpdate on non-squared matrices&quot;</span>&lt;&lt;std::endl ;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            <span class="keywordtype">int</span> i,j,n= sigmaTheta-&gt;size1 ;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            <span class="keywordtype">double</span> tmp ;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            gsl_matrix *U = gsl_matrix_alloc(n,n) ;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            gsl_vector *D = gsl_vector_alloc(n) ;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            gsl_vector *y = gsl_vector_alloc(n) ;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            <span class="comment">// A first thing is to set SS&#39; (chol factor) in a LU form, L being unitriangular</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;            <span class="comment">// Compute U = L^T and D = diag(L)</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            gsl_matrix_set_zero(U) ;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            <span class="keywordflow">for</span> (i=0; i&lt;n; i++){</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                gsl_vector_set(D,i,gsl_matrix_get(sigmaTheta,i,i));</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                <span class="keywordflow">for</span> (j=0; j&lt;=i; j++){</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                    gsl_matrix_set(U,j,i,gsl_matrix_get(sigmaTheta,i,j));</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                }</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;            }</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;            <span class="comment">// Replace L by L*D^{-1} and U by D*U</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            <span class="keywordflow">for</span> (i=0; i&lt;n; i++){</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                <span class="keywordflow">for</span> (j=0; j&lt;=i; j++){</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                    tmp = gsl_matrix_get(sigmaTheta,i,j);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                    tmp /= gsl_vector_get(D,j);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                    gsl_matrix_set(sigmaTheta,i,j,tmp);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                    tmp = gsl_matrix_get(U,j,i);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                    tmp *= gsl_vector_get(D,j);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                    gsl_matrix_set(U,j,i,tmp);</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                }</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            }</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            <span class="comment">// compute the y = alpha x vector</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            gsl_vector_memcpy(y,x) ;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            gsl_vector_scale(y,alpha) ;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            <span class="comment">// perform the rank 1 LU modification</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;            <span class="keywordflow">for</span> (i=0; i&lt;n; i++){</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                <span class="comment">// diagonal update</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                tmp = gsl_matrix_get(U,i,i) +</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                      gsl_vector_get(x,i)*gsl_vector_get(y,i);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                gsl_matrix_set(U,i,i,tmp);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                tmp = gsl_vector_get(y,i);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                tmp /= gsl_matrix_get(U,i,i);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                gsl_vector_set(y,i,tmp);</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                <span class="keywordflow">for</span> (j=i+1; j&lt;n; j++){</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                    <span class="comment">// L (that is sigmaTheta) update</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                    tmp = gsl_vector_get(x,j) -</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                          gsl_vector_get(x,i)*gsl_matrix_get(sigmaTheta,j,i);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                    gsl_vector_set(x,j,tmp) ;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;                    tmp = gsl_matrix_get(sigmaTheta,j,i) + gsl_vector_get(y,i) * gsl_vector_get(x,j);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;                    gsl_matrix_set(sigmaTheta,j,i,tmp);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;                }</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;                <span class="keywordflow">for</span> (j=i+1; j&lt;n; j++) {</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;                    <span class="comment">// U update</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;                    tmp = gsl_matrix_get(U,i,j) +</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;                          gsl_vector_get(x,i)*gsl_vector_get(y,j);</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;                    gsl_matrix_set(U,i,j,tmp) ;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;                    tmp = gsl_vector_get(y,j) -</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                          gsl_vector_get(y,i) * gsl_matrix_get(U,i,j);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                    gsl_vector_set(y,j,tmp) ;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;                }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            }</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="comment">// Now we want the chol decomposition</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;            <span class="comment">// first D = sqrt(diag(U)) ;</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="keywordflow">for</span> (i=0; i&lt;n; i++){</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;                tmp =  gsl_matrix_get(U,i,i) ;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;                <span class="keywordflow">if</span> (tmp&lt;=0){std::cout&lt;&lt; <span class="stringliteral">&quot;WARNING ukf::math::choleskyUpdate::matrix not positive definite  : &quot;</span> &lt;&lt; tmp &lt;&lt; std::endl;}</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;                gsl_vector_set(D,i,sqrt(tmp)) ;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;            }</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="comment">// then L = L*D ;</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;            <span class="keywordflow">for</span> (i=0; i&lt;n; i++) {</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                <span class="keywordflow">for</span> (j=0; j&lt;n; j++) {</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                    tmp = gsl_matrix_get(sigmaTheta,i,j) * gsl_vector_get(D,j);</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;                    gsl_matrix_set(sigmaTheta,i,j,tmp);</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;            }</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            <span class="comment">// that&#39;s all folks !</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            <span class="comment">//free memory</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            gsl_matrix_free(U);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            gsl_vector_free(y);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;            gsl_vector_free(D);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    }  <span class="comment">// math</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;}  <span class="comment">// ukf</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="preprocessor">#endif  // UKF_MATH_H</span></div>
<div class="ttc" id="namespaceukf_1_1math_html_acaa2c088a31957c32107da9c838c77bb"><div class="ttname"><a href="namespaceukf_1_1math.html#acaa2c088a31957c32107da9c838c77bb">ukf::math::min</a></div><div class="ttdeci">double min(double a, double b)</div><div class="ttdef"><b>Definition:</b> ukf_math.h:35</div></div>
<div class="ttc" id="namespaceukf_1_1math_html_a1a77efe08924024899592af61ec193da"><div class="ttname"><a href="namespaceukf_1_1math.html#a1a77efe08924024899592af61ec193da">ukf::math::cmp_diff</a></div><div class="ttdeci">bool cmp_diff(double x, double y)</div><div class="ttdef"><b>Definition:</b> ukf_math.h:54</div></div>
<div class="ttc" id="namespaceukf_1_1math_html_ac921eed0b4618cb2e860cf712c676675"><div class="ttname"><a href="namespaceukf_1_1math.html#ac921eed0b4618cb2e860cf712c676675">ukf::math::choleskyUpdate</a></div><div class="ttdeci">void choleskyUpdate(gsl_matrix *sigmaTheta, double alpha, gsl_vector *x)</div><div class="ttdoc">This function performs a cholesky update according to Strange et al.(2007) </div><div class="ttdef"><b>Definition:</b> ukf_math.h:64</div></div>
<div class="ttc" id="namespaceukf_1_1math_html_af4ef51ae6ef8c8d19eba957802834d4d"><div class="ttname"><a href="namespaceukf_1_1math.html#af4ef51ae6ef8c8d19eba957802834d4d">ukf::math::max</a></div><div class="ttdeci">double max(double a, double b)</div><div class="ttdef"><b>Definition:</b> ukf_math.h:40</div></div>
<div class="ttc" id="namespaceukf_1_1math_html_a8123c498310baa12b0985a3bd271c06c"><div class="ttname"><a href="namespaceukf_1_1math.html#a8123c498310baa12b0985a3bd271c06c">ukf::math::signof</a></div><div class="ttdeci">double signof(double x)</div><div class="ttdef"><b>Definition:</b> ukf_math.h:45</div></div>
<div class="ttc" id="namespaceukf_1_1math_html_a341c355f5fddc026efa8589de2f59a50"><div class="ttname"><a href="namespaceukf_1_1math.html#a341c355f5fddc026efa8589de2f59a50">ukf::math::cmp_equal</a></div><div class="ttdeci">bool cmp_equal(double x, double y)</div><div class="ttdef"><b>Definition:</b> ukf_math.h:50</div></div>
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